Re: Integral points on elliptic curves
- To: mathgroup at smc.vnet.net
- Subject: [mg122515] Re: Integral points on elliptic curves
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sun, 30 Oct 2011 04:25:19 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <j80q8p$adb$1@smc.vnet.net> <j862sg$5v7$1@smc.vnet.net> <201110262140.RAA00128@smc.vnet.net> <j8dthn$kga$1@smc.vnet.net> <201110291112.HAA05405@smc.vnet.net>
On 29 Oct 2011, at 13:12, Costa Bravo wrote: > Andrzej Kozlowski wrote: > >>> In[60]:= k = 1641843; >>> AbsoluteTiming[y0 = Ceiling[k^(1/3)]; >>> Do[If[FractionalPart[Sqrt[y^3 - k]] == 0,Print[Sqrt[y^3 - k], " ", y]], {y, y0, 10000}]] >>> >>> 468 123 >>> 11754 519 >>> >>> Out[61]= {3.4375000, Null} >>> >>> -- >>> Costa >>> >> >> This is hardly impressive when compared with: >> >> Solve[y^3 - x^2 == 1641843&& 0< x&& 0< y< 10^3, {x, y}, >> Integers] // Timing >> >> {0.383947,{{x->468,y->123},{x->11754,y->519}}} >> >> Andrzej Kozlowski > > O , You have y<10^3 I have y <= 10 000 !! > > Solve[y^3 - x^2 == 1641843&& 0< x&& 0< y< 10^4, {x, y}, > Integers] // Timing > > {10.22, {{x -> 468, y -> 123}, {x -> 11754, y -> 519}}} > > This is hardly impressive ;) > > If in your algorithm, we take y< 2*10^4 -> Solve::svars ! > > -- > Costa > SetSystemOptions[ "ReduceOptions" -> {"ExhaustiveSearchMaxPoints" -> {1000, 10^6}}]; Solve[y^3 - x^2 == 1641843 && 0 < x && 0 < y < 10^6, {x, y}, Integers] // Timing {1050.14,{{x->468,y->123},{x->11754,y->519}}} Andrzej Kozlowski
- References:
- Re: Integral points on elliptic curves
- From: Costa Bravo <q13a27tt@aol.com>
- Re: Integral points on elliptic curves
- From: Costa Bravo <q13a27tt@aol.com>
- Re: Integral points on elliptic curves